Bill and his daughter Susan are both standing on identical skateboards (with really good frictionless ball bearings), initially at rest. Bill weighs three times as much as Susan. Bill pushes
Horizontally on Susan's back, causing Susan to start moving away from Bill. Just after Bill stops
Pushing,
A) Susan and Bill are moving away from each other, and Susan's speed is one-third that of Bill.
B) Susan and Bill are moving away from each other, with equal speeds.
C) Susan and Bill are moving away from each other, and Susan's speed is three times that of Bill.
D) Susan is moving away from Bill, and Bill is stationary.

Question

Quizplus · Accepted Answer

According to the conservation of momentum, when Bill pushes Susan, the total momentum of the system (Bill and Susan) must remain constant. Since momentum is the product of mass and velocity, and Bill has three times the mass of Susan, for their momentums to be equal and opposite (thus conserving the total momentum at zero, as they started at rest), Susan must move away with a velocity that is three times that of Bill's.

Bill and His Daughter Susan Are Both Standing on Identical